20A.1 As we saw earlier, if the switch is made, an extra 100 units per period will be sold at a gross profit of $175 − 130 5 $45 each. The total benefit is thus $45 3 100 5 $4,500 per period. At 2.0 percent per period forever, the PV is $4,500y.02 5 $225,000. The cost of the switch is equal to this period’s revenue of $175 3 1,000 units 5 $175,000 plus the cost of producing the extra 100 units, 100 3 $130 5 $13,000. The total cost is thus $188,000, and the NPV is $225,000 2 188,000 5 $37,000. The switch should be made. For the accounts receivable approach, we interpret the $188,000 cost as the investment in receivables. At 2.0 percent per period, the carrying cost is $188,000 3 .02 5 $3,760 per period. The benefit per period we calculated as $4,500; so the net gain per period is $4,500 2 3,760 5 $740. At 2.0 percent per period, the PV of this is $740y.02 5 $37,000. Finally, for the one-shot approach, if credit is not granted, the firm will generate ($175 2 130) 3 1,000 5 $45,000 this period. If credit is extended, the firm will invest $130 3 1,100 5 $143,000 today and receive $175 3 1,100 5 $192,500 in one period. The NPV of this second option is $192,500y1.02 2 143,000 5 $45,725.49. The firm is $45,725.49 2 45,000 5 $725.49 better off today and in each future period because of granting credit. The PV of this stream is $725.49 1 725.49y.02 5 $37,000 (allowing for a rounding error).
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